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Home >> Algebraic Expression >> Addition Expression (Algebra) >>

Addition Expression in Algebra

Addition Expression (Algebra) Division Expression (Algebra) Multipication Expression (Algebra) Subtraction Expression (Algebra) Terms of Algebraic Expression
Value of an Algebraic Expression Tree Diagram for Algebraic Expression Constants Variables

  • What is Addition Expression

    Explanation :- Addition Expression in algebra includes:

    Literal Number,
    Addition Operator (+)
    and Constant

    For example:
    (x + y), (a + 7), (4 + b)

    In the above example, we have :-
    Addition Operator i.e. plus sign (+),
    Literal Numbers = x, y, a & b.
    Constants = 7 & 4.

    Addition expression in algebra is of the following two types:-

    1). Sum of Literal Numbers :- It includes Addition Operator (+) and two or more Literal Numbers.
    For example = x+y , p+q, a+b+c
    In the above example we have :-
    Addition Operator = (+),
    Literal Numbers =. x, y, p, q, a, b & c
    Note :- In such an expression, we don't have any Constants.

    2). Sum of Literal Numbers and Constants :- It includes Addition Operator (+), Literal Numbers and Constants.
    For example = x+7 , 8+a, p+q+5...
    In the above example we have :-
    Addition Operator = (+),
    Literal Numbers = x, p, q & a.
    Constants = 7, 8 & 5.






  • Addition of Algebraic Expressions

    Before you further read, you are advice to read:

    What are Terms of Algebraic Expression ?
    What are Like Terms ?
    What are Unlike Terms ?
    Addition of Like Terms ?

    During addition of algebraic expression we are encountered with the following three situations:

  • Addition of algebraic expression having like terms
  • Addition of algebraic expression having unlike terms
  • Addition of algebraic expression having both like and unlike terms

    1) Addition of algebraic expression having like terms

    Following are steps to be followed while adding two or more algebraic Expression having like terms:

    Step 1: Rearrange the terms of given algebraic expression into like-terms
    Step 2: Add like terms

    Example : Add 2a + 3b 4x + 5y 6 and (-7a - 8b + 9x + 10y 11)
    Solution: Given two algebraic expression

    First Algebraic expression = 2a + 3b 4x + 5y 6
    Second Algebraic expression = (-7a - 8b + 9x + 10y 11)

    Now addition of given algebraic expression is done as follows:
    (2a + 3b 4x + 5y 6) + (-7a - 8b + 9x + 10y 11)

    Open brackets and we get:
    = 2a + 3b 4x + 5y 6 - 7a - 8b + 9x + 10y 11

    Rearrange the terms of given algebraic expression into like-terms and we get:
    = 2a 7a + 3b 8b 4x + 9x + 5y + 10y 6 11

    Add like terms and we get:
    = (5a 5b + 3x + 15y 17)

    Hence, (2a + 3b 4x + 5y 6) + (-7a - 8b + 9x + 10y 11) = (5a 5b + 3x + 15y 17)


    2) Addition of algebraic expression having unlike terms

    Here we must note that two or more algebraic expressions are added only when both have unlike terms.
    Or we can also say that:
    Algebraic expressions having unlike terms cannot be added.
    E.g. 2x 1 + 3z, 3y + 5t 9a + 5x2, 10p + t3 - 4b 8r, 32q 6m + 10c cannot be added because all have unlike terms.


    3) Addition of algebraic expression having both like and unlike terms

    In such situations you will notice that algebraic expressions which are to be added have like as well as unlike terms. So in such situations we add like terms and keep unlike terms as such.

    Example : Add ( 2x3 + 3x2 + 10y 2), x3 - 4x2 + 9x - c
    Solution: Given two algebraic expression

    First Algebraic expression = 2x3 + 3x2 + 10y - 2
    Second Algebraic expression = x3 - 4x2 + 9x - c

    Now addition of given algebraic expression is done as follows:
    ( 2x3 + 3x2 + 10y 2) + (x3 - 4x2 + 9x c)

    Open brackets and we get:
    = 2x3 + 3x2 + 10y 2 + x3 - 4x2 + 9x c

    Rearrange them into like terms and unlike terms & we get
    = 2x3 + x3 + 3x2 - 4x2 + 10y + 9x c 2

    Add like terms and keep unlike terms as such & we get:
    = x3 - x2 + 10y + 9x c - 2

    Hence, ( 2x3 + 3x2 + 10y 2) + (x3 - 4x2 + 9x c) = ( x3 - x2 + 10y + 9x c 2)



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